details

property	value
status	complete
benchmark	sipma91.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n046.star.cs.uiowa.edu
space	WTC

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.88699 seconds
cpu usage	8.57321
user time	8.09259
system time	0.480618
max virtual memory	3.6437712E7
max residence set size	225888.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

8.38/4.85 WORST_CASE(Omega(n^1), O(n^2)) 8.38/4.86 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 8.38/4.86 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 8.38/4.86 8.38/4.86 8.38/4.86 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, max(6, 24354 + -221 * Arg_0) + nat(101 + -1 * Arg_0) + nat(111 + -1 * Arg_0) + nat(60702 + -551 * Arg_0) + max(113 + -1 * Arg_0, 2) + nat(max(113 + -1 * Arg_0, 2) * max(-183, 24348 + -221 * Arg_0) + nat(24348 + -221 * Arg_0) * max(-183, 24348 + -221 * Arg_0)) + max(4, 448 + -4 * Arg_0) + nat(max(1, 112 + -1 * Arg_0) * max(-183, 24348 + -221 * Arg_0) + nat(24348 + -221 * Arg_0) * max(-183, 24348 + -221 * Arg_0))). 8.38/4.86 8.38/4.86 (0) CpxIntTrs 8.38/4.86 (1) Koat2 Proof [FINISHED, 3138 ms] 8.38/4.86 (2) BOUNDS(1, max(6, 24354 + -221 * Arg_0) + nat(101 + -1 * Arg_0) + nat(111 + -1 * Arg_0) + nat(60702 + -551 * Arg_0) + max(113 + -1 * Arg_0, 2) + nat(max(113 + -1 * Arg_0, 2) * max(-183, 24348 + -221 * Arg_0) + nat(24348 + -221 * Arg_0) * max(-183, 24348 + -221 * Arg_0)) + max(4, 448 + -4 * Arg_0) + nat(max(1, 112 + -1 * Arg_0) * max(-183, 24348 + -221 * Arg_0) + nat(24348 + -221 * Arg_0) * max(-183, 24348 + -221 * Arg_0))) 8.38/4.86 (3) Loat Proof [FINISHED, 599 ms] 8.38/4.86 (4) BOUNDS(n^1, INF) 8.38/4.86 8.38/4.86 8.38/4.86 ---------------------------------------- 8.38/4.86 8.38/4.86 (0) 8.38/4.86 Obligation: 8.38/4.86 Complexity Int TRS consisting of the following rules: 8.38/4.86 evalsipma91start(A, B, C, D) -> Com_1(evalsipma91entryin(A, B, C, D)) :|: TRUE 8.38/4.86 evalsipma91entryin(A, B, C, D) -> Com_1(evalsipma91returnin(A, B, C, D)) :|: A >= 101 8.38/4.86 evalsipma91entryin(A, B, C, D) -> Com_1(evalsipma91bb3in(1, A, C, D)) :|: 100 >= A 8.38/4.86 evalsipma91bb3in(A, B, C, D) -> Com_1(evalsipma91bb2in(A, B, C, D)) :|: 100 >= B 8.38/4.86 evalsipma91bb3in(A, B, C, D) -> Com_1(evalsipma91bb11in(A, B, C, D)) :|: B >= 101 8.38/4.86 evalsipma91bb2in(A, B, C, D) -> Com_1(evalsipma91bb3in(A + 1, B + 11, C, D)) :|: TRUE 8.38/4.86 evalsipma91bb11in(A, B, C, D) -> Com_1(evalsipma91bb5in(A, B, C, D)) :|: A >= 2 8.38/4.86 evalsipma91bb11in(A, B, C, D) -> Com_1(evalsipma91returnin(A, B, C, D)) :|: 1 >= A 8.38/4.86 evalsipma91bb5in(A, B, C, D) -> Com_1(evalsipma91bb8in(A, B, B - 10, A - 1)) :|: 110 >= B 8.38/4.86 evalsipma91bb5in(A, B, C, D) -> Com_1(evalsipma91bb8in(A, B, B - 10, A - 1)) :|: 1 >= A 8.38/4.86 evalsipma91bb5in(A, B, C, D) -> Com_1(evalsipma91bb8in(A, B, B - 10, A - 1)) :|: A >= 3 8.38/4.86 evalsipma91bb5in(A, B, C, D) -> Com_1(evalsipma91bb11in(A - 1, B - 10, C, D)) :|: B >= 111 && A >= 2 && A <= 2 8.38/4.86 evalsipma91bb8in(A, B, C, D) -> Com_1(evalsipma91bb11in(D, C + 1, C, D)) :|: C >= 101 8.38/4.86 evalsipma91bb8in(A, B, C, D) -> Com_1(evalsipma91bb11in(D, C + 11, C, D)) :|: C >= 101 && 100 >= C 8.38/4.86 evalsipma91bb8in(A, B, C, D) -> Com_1(evalsipma91bb11in(D + 1, C + 1, C, D)) :|: 100 >= C && C >= 101 8.38/4.86 evalsipma91bb8in(A, B, C, D) -> Com_1(evalsipma91bb11in(D + 1, C + 11, C, D)) :|: 100 >= C 8.38/4.86 evalsipma91returnin(A, B, C, D) -> Com_1(evalsipma91stop(A, B, C, D)) :|: TRUE 8.38/4.86 8.38/4.86 The start-symbols are:[evalsipma91start_4] 8.38/4.86 8.38/4.86 8.38/4.86 ---------------------------------------- 8.38/4.86 8.38/4.86 (1) Koat2 Proof (FINISHED) 8.38/4.86 YES( ?, 6+max([0, max([-183, -404+221*max([1, 112-Arg_0])])])+max([0, 101-Arg_0])+max([2, 2*max([1, 112-Arg_0])])+max([1, 112-Arg_0])+max([0, (max([1, 112-Arg_0])+max([0, max([-183, -404+221*max([1, 112-Arg_0])])]))*max([-183, -404+221*max([1, 112-Arg_0])])])+max([0, 111-Arg_0])+max([0, max([-459, -1010+551*max([1, 112-Arg_0])])])+max([0, (1+max([1, 112-Arg_0])+max([0, max([-183, -404+221*max([1, 112-Arg_0])])]))*max([-183, -404+221*max([1, 112-Arg_0])])])+max([1, 112-Arg_0])+max([2, 113-Arg_0]) {O(n^2)}) 8.38/4.86 8.38/4.86 8.38/4.86 8.38/4.86 Initial Complexity Problem: 8.38/4.86 8.38/4.86 Start: evalsipma91start 8.38/4.86 8.38/4.86 Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3 8.38/4.86 8.38/4.86 Temp_Vars: 8.38/4.86 8.38/4.86 Locations: evalsipma91bb11in, evalsipma91bb2in, evalsipma91bb3in, evalsipma91bb5in, evalsipma91bb8in, evalsipma91entryin, evalsipma91returnin, evalsipma91start, evalsipma91stop 8.38/4.86 8.38/4.86 Transitions: 8.38/4.86 8.38/4.86 evalsipma91bb11in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91bb5in(Arg_0,Arg_1,Arg_2,Arg_3):|:101 <= Arg_1 && 102 <= Arg_0+Arg_1 && 1 <= Arg_0 && 2 <= Arg_0 8.38/4.86 8.38/4.86 evalsipma91bb11in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91returnin(Arg_0,Arg_1,Arg_2,Arg_3):|:101 <= Arg_1 && 102 <= Arg_0+Arg_1 && 1 <= Arg_0 && Arg_0 <= 1 8.38/4.86 8.38/4.86 evalsipma91bb2in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91bb3in(Arg_0+1,Arg_1+11,Arg_2,Arg_3):|:Arg_1 <= 100 && Arg_1 <= 99+Arg_0 && 1 <= Arg_0 8.38/4.86 8.38/4.86 evalsipma91bb3in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91bb11in(Arg_0,Arg_1,Arg_2,Arg_3):|:1 <= Arg_0 && 101 <= Arg_1 8.38/4.86 8.38/4.86 evalsipma91bb3in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91bb2in(Arg_0,Arg_1,Arg_2,Arg_3):|:1 <= Arg_0 && Arg_1 <= 100 8.38/4.86 8.38/4.86 evalsipma91bb5in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91bb11in(Arg_0-1,Arg_1-10,Arg_2,Arg_3):|:101 <= Arg_1 && 103 <= Arg_0+Arg_1 && 2 <= Arg_0 && 111 <= Arg_1 && Arg_0 <= 2 && 2 <= Arg_0 8.38/4.86 8.38/4.86 evalsipma91bb5in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91bb8in(Arg_0,Arg_1,Arg_1-10,Arg_0-1):|:101 <= Arg_1 && 103 <= Arg_0+Arg_1 && 2 <= Arg_0 && Arg_1 <= 110 8.38/4.86 8.38/4.86 evalsipma91bb5in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91bb8in(Arg_0,Arg_1,Arg_1-10,Arg_0-1):|:101 <= Arg_1 && 103 <= Arg_0+Arg_1 && 2 <= Arg_0 && 3 <= Arg_0 8.38/4.86 8.38/4.86 evalsipma91bb8in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91bb11in(Arg_3,Arg_2+1,Arg_2,Arg_3):|:1+Arg_3 <= Arg_0 && 1 <= Arg_3 && 92 <= Arg_2+Arg_3 && 102 <= Arg_1+Arg_3 && 3 <= Arg_0+Arg_3 && Arg_0 <= 1+Arg_3 && 10+Arg_2 <= Arg_1 && 91 <= Arg_2 && 192 <= Arg_1+Arg_2 && Arg_1 <= 10+Arg_2 && 93 <= Arg_0+Arg_2 && 101 <= Arg_1 && 103 <= Arg_0+Arg_1 && 2 <= Arg_0 && 101 <= Arg_2 8.38/4.86 8.38/4.86 evalsipma91bb8in(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91bb11in(Arg_3+1,Arg_2+11,Arg_2,Arg_3):|:1+Arg_3 <= Arg_0 && 1 <= Arg_3 && 92 <= Arg_2+Arg_3 && 102 <= Arg_1+Arg_3 && 3 <= Arg_0+Arg_3 && Arg_0 <= 1+Arg_3 && 10+Arg_2 <= Arg_1 && 91 <= Arg_2 && 192 <= Arg_1+Arg_2 && Arg_1 <= 10+Arg_2 && 93 <= Arg_0+Arg_2 && 101 <= Arg_1 && 103 <= Arg_0+Arg_1 && 2 <= Arg_0 && Arg_2 <= 100 8.38/4.86 8.38/4.86 evalsipma91entryin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91bb3in(1,Arg_0,Arg_2,Arg_3):|:Arg_0 <= 100 8.38/4.86 8.38/4.86 evalsipma91entryin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91returnin(Arg_0,Arg_1,Arg_2,Arg_3):|:101 <= Arg_0 8.38/4.86 8.38/4.86 evalsipma91returnin(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91stop(Arg_0,Arg_1,Arg_2,Arg_3):|: 8.38/4.86 8.38/4.86 evalsipma91start(Arg_0,Arg_1,Arg_2,Arg_3) -> evalsipma91entryin(Arg_0,Arg_1,Arg_2,Arg_3):|: 8.38/4.86 8.38/4.86 8.38/4.86 8.38/4.86 Timebounds: 8.38/4.86 8.38/4.86 Overall timebound: 6+max([0, max([-183, -404+221*max([1, 112-Arg_0])])])+max([0, 101-Arg_0])+max([2, 2*max([1, 112-Arg_0])])+max([1, 112-Arg_0])+max([0, (max([1, 112-Arg_0])+max([0, max([-183, -404+221*max([1, 112-Arg_0])])]))*max([-183, -404+221*max([1, 112-Arg_0])])])+max([0, 111-Arg_0])+max([0, max([-459, -1010+551*max([1, 112-Arg_0])])])+max([0, (1+max([1, 112-Arg_0])+max([0, max([-183, -404+221*max([1, 112-Arg_0])])]))*max([-183, -404+221*max([1, 112-Arg_0])])])+max([1, 112-Arg_0])+max([2, 113-Arg_0]) {O(n^2)} 8.38/4.86 8.38/4.86 6: evalsipma91bb11in->evalsipma91bb5in: max([0, (1+max([1, 112-Arg_0])+max([0, max([-183, -404+221*max([1, 112-Arg_0])])]))*max([-183, -404+221*max([1, 112-Arg_0])])])+max([2, 113-Arg_0]) {O(n^2)} 8.38/4.86 8.38/4.86 7: evalsipma91bb11in->evalsipma91returnin: 1 {O(1)} 8.38/4.86 8.38/4.86 5: evalsipma91bb2in->evalsipma91bb3in: max([0, 111-Arg_0]) {O(n)} 8.38/4.86 8.38/4.86 3: evalsipma91bb3in->evalsipma91bb2in: max([0, 101-Arg_0]) {O(n)} popout

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all output return to Complexity_ITS 2019-03-21 04.46